SOLUTION: Michael's bank contains only nickels, dimes and quarters. There are 63 coins in all valued at $5.50. The number of nickels is 5 short of being 3 times the sum of the number of dime

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Question 832822: Michael's bank contains only nickels, dimes and quarters. There are 63 coins in all valued at $5.50. The number of nickels is 5 short of being 3 times the sum of the number of dimes and quarters. How many dimes are in the bank
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Michael's bank contains only nickels, dimes and quarters.
N = number of nickels
D = number of dimes
Q = the number of quarters
There are 63 coins in all
           N + D + Q = 63
valued at $5.50.
The N nickels are worth $0.05N
The D dimes are worth $0.10D
The Q quarters are worth $0.25Q

0.05N + 0.10D + .25Q = 5.50

Multiply every term by 100 moves the decimals two places over:

      5N + 10D + 25Q = 550

Divide every term by 5

         N + 5D + 5Q = 110
The number of nickels is 5 short of being 3 times the sum of
the number of dimes and quarters.
the sum of number of dimes and quarters = D+Q
3 times the sum of number of dimes and quarters = 3(D+Q)
5 short of being 3 times the sum of the number of dimes and quarters = 3(D+Q)-5
So

                   N = 3(D+Q) - 5
                   N = 3D + 3Q - 5
         N - 3D - 3Q = -5

So we have the system of 3 equations in 3 unknowns:

         N +  D +  Q =  63
         N + 2D + 5Q = 110 
         N - 3D - 3Q =  -5

Solve that system by elimination.
How many dimes are in the bank?
Solve the system and see.  If you can't post again
asking how to solve it.

Edwin
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